Finite Group DatabasebetaFinite Group Databasebeta| order | 6616 |
| automorphism | Aut(G) order 5464816 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1654 |
| unambiguous semidirect product | C827⋊Q8 |
| Sylow | C827 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D827 |
| commutator, socle | C2×C827 | C22 |
| Fitting | C4×C827 | C2 |
| hypercenter | C4 | D827 |
| hypocenter | C827 | Q8 |
| LCS | G ▷ C2×C827 ▷ C827 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,827|a^2=c,b^2=c,b^a=bc,d^b=d^8261657 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27210309, #27210310, #27210311, … |
| maximal normal subgroup of | #27210309, #27210310, #27210311, … |
| maximal quotient of | Dic827⋊C4, C4⋊Dic827, C2×Dic1654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6616, 11);